Key subgroups in topological groups and minimality conditions

Speaker
Michael Megrelishvili (Department of Mathematics, Bar-Ilan University)
Date
29/06/2025 - 13:00 - 12:00Add to Calendar 2025-06-29 12:00:40 2025-06-29 13:00:00 Key subgroups in topological groups and minimality conditions This talk reviews several old and new minimality conditions in topological groups with a focuson the so-called key subgroups. We discuss motivating examples in generalized Heisenberg groups. Extending some results of a joint work with E. Glasner, we continue to studythe Polish group G=Aut(Q/Z) of all circular order preserving permutations of the rational discrete circle.We show that certain extremely amenable subgroups H  in G are inj-key (distinguishweaker Hausdorff group topologies on G) but are not co-minimal in G.This example answers a question from a recent joint work with M. Shlossbergand is inspired by a question proposed by V. Pestov.The talk will conclude with a discussion of related open questions. Presumably, it will be held in person in math seminar room (building 216, room 201) and also on-line via zoom with the link https://biu-ac-il.zoom.us/j/82747834707 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Presumably, it will be held in person in math seminar room (building 216, room 201) and also on-line via zoom with the link https://biu-ac-il.zoom.us/j/82747834707
Abstract

This talk reviews several old and new minimality conditions in topological groups with a focus
on the so-called key subgroups. We discuss motivating examples in generalized Heisenberg
 groups. Extending some results of a joint work with E. Glasner, we continue to study
the Polish group G=Aut(Q/Z) of all circular order preserving permutations of the rational discrete circle.
We show that certain extremely amenable subgroups H  in G are inj-key (distinguish
weaker Hausdorff group topologies on G) but are not co-minimal in G.
This example answers a question from a recent joint work with M. Shlossberg
and is inspired by a question proposed by V. Pestov.
The talk will conclude with a discussion of related open questions.

תאריך עדכון אחרון : 26/06/2025